Question

cone A is similar to cone B cone A has a radius equal to 6 inches in Cone B has a radius equal to 13 in if the volume of cone is 252 in what is the volume of a Cone B

Answer 1

If cone A is similar to cone B, this means that the ratio height/radius is the same in both cones. The formula for the volume of a cone is pi times r^3 times height times 1/3. The measures of the cones known so far are the following:

$r_a=6\text{ in}$$r_b=13\text{ in}$$v_a=252in^3$$v_a=252=\frac{1}{3}\cdot\pi\cdot6^3\cdot h_a$

Then, the height of cone a can be found as:

$h_a=252\cdot3\cdot\frac{1}{\pi\cdot216}\cong1.11$$\frac{1.11}{6}=\frac{h_b}{13}\Rightarrow h_b=2.41$$v_b=\pi\cdot\frac{1}{3}\cdot2.41\cdot13^3=5533.5in^3$